People can be unified even if they live in multiple countries. It depends I guess on how you define yourself. The Latin culture exist in dozens of countries, and there are subtle variations from place to place, but it is essentially one culture. We are a people.
A world can have one government, or thousands. The people of that world can be united regardless of the number of organizations
providing services and protections within a particular geographic area..
As long as a world can in some fashion select a mouthpiece to speak on it behalf in the Federation's governing body, that should be good enought.